Recent advances in artificial intelligence have seen Large Language Models (LLMs) demonstrate notable proficiency in causal discovery tasks. This study explores the factors influencing the performance of LLMs in causal discovery tasks. Utilizing open-source LLMs, we examine how the frequency of causal relations within their pre-training corpora affects their ability to accurately respond to causal discovery queries. Our findings reveal that a higher frequency of causal mentions correlates with better model performance, suggesting that extensive exposure to causal information during training enhances the models' causal discovery capabilities. Additionally, we investigate the impact of context on the validity of causal relations. Our results indicate that LLMs might exhibit divergent predictions for identical causal relations when presented in different contexts. This paper provides the first comprehensive analysis of how different factors contribute to LLM performance in causal discovery tasks.

Thus, word segmentation is important and is influential in many fields including developing text processing applications, such as Information Extraction, Document Summarization, Machine Translation (MT), Natural Language Processing, Information Retrieval, Language Modeling, and Speech Recognition.(15) Word segmentation is often a vital task of language processing. In addition, the reason why word segmentation is significant in the field of Natural Language Processing is because it is the initial step for most higher level natural language processing tasks, such as part-of-speech tagging and parsing. In addition, for languages that are space-delimited such as English or Russian, these languages are being segmented differently as opposed to those that don't have explicit word boundary delimiters, such as Chinese and Japanese. There is a common goal for this task, which is to have a near-perfect word segmentation system, which can still perform reasonably with no or minimum language-specific adaptations (9).

The presence of unobserved common causes and the presence of measurement error are two of the most limiting challenges in the task of causal structure learning. Ignoring either of the two challenges can lead to detecting spurious causal links among variables of interest. In this paper, we study the problem of causal discovery in systems where these two challenges can be present simultaneously. We consider linear models which include four types of variables: variables that are directly observed, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. We characterize the extent of identifiability of such model under separability condition (i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables is identifiable) together with two versions of faithfulness assumptions and propose a notion of observational equivalence. We provide graphical characterization of the models that are equivalent and present a recovery algorithm that could return models equivalent to the ground truth.

As service systems grow increasingly complex and dynamic, many interventions become localized, available and taking effect only in specific states. This paper investigates experiments with local treatments on a widely-used class of dynamic models, Markov Decision Processes (MDPs). Particularly, we focus on utilizing the local structure to improve the inference efficiency of the average treatment effect. We begin by demonstrating the efficiency of classical inference methods, including model-based estimation and temporal difference learning under a fixed policy, as well as classical A/B testing with general treatments. We then introduce a variance reduction technique that exploits the local treatment structure by sharing information for states unaffected by the treatment policy. Our new estimator effectively overcomes the variance lower bound for general treatments while matching the more stringent lower bound incorporating the local treatment structure. Furthermore, our estimator can optimally achieve a linear reduction with the number of test arms for a major part of the variance. Finally, we explore scenarios with perfect knowledge of the control arm and design estimators that further improve inference efficiency.

In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range dependency method for SNLDS. The cornerstone of our approach is the fusion of S4 and SNLDS, leveraging the strengths of both models to effectively address the intricacies of long-range dependencies in switching time series. Through rigorous testing, we demonstrate that our proposed methodology adeptly segments and reproduces long-range dependencies in both the 1-D Lorenz dataset and the 2-D bouncing ball dataset. Notably, our integrated approach outperforms the standalone SNLDS in these tasks.

We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive distributions with a pre-specified probability. Furthermore, we propose, Trust-Bayes, a novel optimization framework for Bayesian meta learning which is cognizant of trustworthy uncertainty quantification without explicit assumptions on the prior model/distribution of the functions. We characterize the lower bounds of the probabilities of the ground truth being captured by the specified intervals and analyze the sample complexity with respect to the feasible probability for trustworthy uncertainty quantification. Monte Carlo simulation of a case study using Gaussian process regression is conducted for verification and comparison with the Meta-prior algorithm.

This paper describes a discrete state-space model -- and accompanying methods -- for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for active inference and learning in a dynamic setting. Specifically, we consider deep or hierarchical forms using the renormalisation group. The ensuing renormalising generative models (RGM) can be regarded as discrete homologues of deep convolutional neural networks or continuous state-space models in generalised coordinates of motion. By construction, these scale-invariant models can be used to learn compositionality over space and time, furnishing models of paths or orbits; i.e., events of increasing temporal depth and itinerancy. This technical note illustrates the automatic discovery, learning and deployment of RGMs using a series of applications. We start with image classification and then consider the compression and generation of movies and music. Finally, we apply the same variational principles to the learning of Atari-like games.

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability distributions. Among these, greedy algorithms for searching the number of clusters by repeatedly splitting or merging clusters have advantages in terms of computation time for problems with large sample sizes. However, studies comparing these methods in systematic evaluation experiments still need to be included. This study examines centroid- and model-based cluster search algorithms in various cases that Gaussian mixture models (GMMs) can generate. The cases are generated by combining five factors: dimensionality, sample size, the number of clusters, cluster overlap, and covariance type. The results show that some cluster-splitting criteria based on Euclidean distance make unreasonable decisions when clusters overlap. The results also show that model-based algorithms are insensitive to covariance type and cluster overlap compared to the centroid-based method if the sample size is sufficient. Our cluster search implementation codes are available at https://github.com/lipryou/searchClustK

Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying assumptions lead to computational tractability, these models fail to capture long-range, complex dependence structures that may be harnessed for greater predictive power. To this end, a Bayesian modelling framework is proposed to parsimoniously capture rich dependence structures in categorical sequences, with memory efficiency suitable for real-time processing of data streams. Parsimonious Bayesian context trees are introduced as a form of variable-order Markov model with conjugate prior distributions. The novel framework requires fewer parameters than fixed-order Markov models by dropping redundant dependencies and clustering sequential contexts. Approximate inference on the context tree structure is performed via a computationally efficient model-based agglomerative clustering procedure. The proposed framework is tested on synthetic and real-world data examples, and it outperforms existing sequence models when fitted to real protein sequences and honeypot computer terminal sessions.

In key real-world problems, full state information is sometimes available but only at a high cost, like activating precise yet energy-intensive sensors or consulting humans, thereby compelling the agent to operate under partial observability. For this scenario, we propose AEMS-SR (Anytime Error Minimization Search with State Requests), a principled online planning algorithm tailored for POMDPs with state requests. By representing the search space as a graph instead of a tree, AEMS-SR avoids the exponential growth of the search space originating from state requests. Theoretical analysis demonstrates AEMS-SR's $\varepsilon$-optimality, ensuring solution quality, while empirical evaluations illustrate its effectiveness compared with AEMS and POMCP, two SOTA online planning algorithms. AEMS-SR enables efficient planning in domains characterized by partial observability and costly state requests offering practical benefits across various applications.